What is the prime factorization of 294?

The prime factorization of 294 can be determined by dividing the number by the smallest prime numbers until we reach a quotient of 1.

First, we divide 294 by 2 (the smallest prime number):

• 294 ÷ 2 = 147

Next, we take 147 and divide it by the next smallest prime number, which is 3:

• 147 ÷ 3 = 49

Now, we check the next prime number, which is 7:

• 49 ÷ 7 = 7

Finally, we divide 7 by itself:

• 7 ÷ 7 = 1

Now, we can combine all the prime factors we used in the divisions. The prime factorization of 294 is:

• 2 × 3 × 7 × 7

Or we can write 7 squared:

• 2 × 3 × 7²

So, the complete prime factorization of 294 is 2, 3, and 7 squared.